In the last century, with the inception of various software development industries at around mid-1960’s, the complexities and size of the software have always been a major concern for the industries. The ad-hoc process of development has evolved into a standardized one due to the increase in the size and complexity of software projects. The standardized process of software development was further evolved to predict the overall cost required for the development before the software is actually built. To achieve the same, many cost estimation methodologies have already been successfully implemented, each with certain pros and cons. The present scenario demands even further refined and accurate predictions, which the above-said methods cease to provide. In this paper, we present a chaotically modified particle swarm optimization (CMPSO) based morphological learning approach to accurately estimate the cost incurred in the development process. The proposed approach focuses on a mathematical morphological (MM) framework based hybrid artificial neuron (also called dilation-erosion perceptron or DEP) with algebraic foundations in complete lattice theory (CLT). The proposed CMPSO-DEP model was tested on 5 well-known datasets of software projects with three popular performance metrics and the results were compared with the best existing models available in the literature.